← Back to the Two-way Tables test
Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Standards: 8.SP.A.4 · Level: Grade 8
Question 1 Complete the totals (2 points)
(a) 21 + 14 = 35 and 29 + 26 = 55.
(b) 21 + 29 = 50, 14 + 26 = 40, and 35 + 55 = 90.
Rows 35 and 55; columns 50 and 40; total 90
Scoring: 1 point per part.
Question 2 Row relative frequencies (3 points)
(a) 21 ÷ 35 = 60%
(b) 29 ÷ 55 ≈ 52.7%, so 53%
(c) The percents are 60% and 53%, only 7 points apart: a weak association at most.
Scoring: 1 point per part.
Question 3 Column relative frequencies (3 points)
(a) 21 ÷ 50 = 42%
(b) 14 ÷ 40 = 35%
(c) These divide by column totals (sport or no sport), while Question 2 divided by row totals (job or no job), so they answer different questions.
Scoring: 1 point per part.
Question 4 Build a table from a list (3 points)
(a) (D, Y) appears 5 times, (D, N) 2 times, (C, Y) 2 times, (C, N) 3 times.
| Has sibling | No sibling | Total | |
|---|---|---|---|
| Prefers dogs | 5 | 2 | 7 |
| Prefers cats | 2 | 3 | 5 |
| Total | 7 | 5 | 12 |
(b) The totals are 7 and 5 for the rows, 7 and 5 for the columns, and 12 overall.
Scoring: part (a) 2 points for all four counts (1 point if two or three are correct); part (b) 1 point.
Question 5 Segmented bars (3 points)
(a) Ages 8 to 12 (78% compared with 41%).
(b) The percents differ by 37 points, so yes, there is an association: older riders are less likely to wear a helmet.
Scoring: part (a) 1 point; part (b) 1 point for the comparison, 1 point for the conclusion.
Question 6 Evaluate a claim (2 points)
Adults: 54 ÷ 300 = 18%. Youths: 36 ÷ 150 = 24%.
Ben is not correct: youths are more likely to buy a pass (24% versus 18%)
Scoring: 1 point for each correct percent, with a correct conclusion.
Question 7 Fill in the table (2 points)
Top-right: 90 − 55 = 35. Bottom-left: 100 − 55 = 45. Bottom-right: 70 − 45 = 25 (also 60 − 35 = 25).
35, 45, and 25
Scoring: 1 point for the top-right and bottom-left, 1 point for the bottom-right with a check.
Question 8 No association (2 points)
The percents are almost equal, so the choice in the columns does not depend much on the row group.
There is little or no association
Scoring: 1 point for the conclusion, 1 point for the explanation.